Related papers: Covariance Estimation: The GLM and Regularization …
Estimation of Markov Random Field and covariance models from high-dimensional data represents a canonical problem that has received a lot of attention in the literature. A key assumption, widely employed, is that of {\em sparsity} of the…
In the last two decades, the linear model of coregionalization (LMC) has been widely used to model multivariate spatial processes. However, it can be a challenging task to conduct likelihood-based inference for such models because of the…
This paper addresses the statistical estimation of Gaussian Mixture Models (GMMs) with unknown diagonal covariances from independent and identically distributed samples. We employ the Beurling-LASSO (BLASSO), a convex optimization framework…
The paper proposes a new covariance estimator for large covariance matrices when the variables have a natural ordering. Using the Cholesky decomposition of the inverse, we impose a banded structure on the Cholesky factor, and select the…
While matrix variate regression models have been studied in many existing works, classical statistical and computational methods for the analysis of the regression coefficient estimation are highly affected by high dimensional and noisy…
Due to the ease of modern data collection, applied statisticians often have access to a large set of covariates that they wish to relate to some observed outcome. Generalized linear models (GLMs) offer a particularly interpretable framework…
Gaussian graphical models (GGMs) are widely used to recover the conditional independence structure among random variables. Recent work has sought to incorporate auxiliary covariates to improve estimation, particularly in applications such…
Recently it has become popular to learn sparse Gaussian graphical models (GGMs) by imposing l1 or group l1,2 penalties on the elements of the precision matrix. Thispenalized likelihood approach results in a tractable convex optimization…
Linear models have found widespread use in statistical investigations. For every linear model there exists a matrix representation for which the ReML (Restricted Maximum Likelihood) can be constructed from the elements of the corresponding…
We consider distributed estimation of the inverse covariance matrix, also called the concentration or precision matrix, in Gaussian graphical models. Traditional centralized estimation often requires global inference of the covariance…
Many problems of low-level computer vision and image processing, such as denoising, deconvolution, tomographic reconstruction or super-resolution, can be addressed by maximizing the posterior distribution of a sparse linear model (SLM). We…
In covariance matrix estimation, one of the challenges lies in finding a suitable model and an efficient estimation method. Two commonly used modelling approaches in the literature involve imposing linear restrictions on the covariance…
Solving l1 regularized optimization problems is common in the fields of computational biology, signal processing and machine learning. Such l1 regularization is utilized to find sparse minimizers of convex functions. A well-known example is…
The generalised linear model (GLM) is a very important tool for analysing real data in biology, sociology, agriculture, engineering and many other application domain where the relationship between the response and explanatory variables may…
Gaussian graphical models (GGM) have been widely used in many high-dimensional applications ranging from biological and financial data to recommender systems. Sparsity in GGM plays a central role both statistically and computationally.…
We study general singular value shrinkage estimators in high-dimensional regression and classification, when the number of features and the sample size both grow proportionally to infinity. We allow models with general covariance matrices…
This paper presents a study on an $\ell_1$-penalized covariance regression method. Conventional approaches in high-dimensional covariance estimation often lack the flexibility to integrate external information. As a remedy, we adopt the…
Convolutional neural networks (CNNs) provide flexible function approximations for a wide variety of applications when the input variables are in the form of images or spatial data. Although CNNs often outperform traditional statistical…
High-dimensional statistical inference deals with models in which the the number of parameters p is comparable to or larger than the sample size n. Since it is usually impossible to obtain consistent procedures unless $p/n\rightarrow0$, a…
The Graphical Lasso (GLasso) algorithm is fast and widely used for estimating sparse precision matrices (Friedman et al., 2008). Its central role in the literature of high-dimensional covariance estimation rivals that of Lasso regression…